Somewhat Homomorphic Encryption Noise Management
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Solution Overview
Problem
Fully homomorphic encryption schemes are impractical due to high computational requirements, making them inefficient, while existing somewhat homomorphic encryption schemes introduce noise that limits the number of homomorphic operations, affecting security and accuracy.
Innovation Solution
A Somewhat Homomorphic Encryption (SHE) scheme is developed that uses a public key and private key-based asymmetric encryption, incorporating HOM_XOR and HOM_AND operators to perform calculations on encrypted data without decrypting, with noise management to maintain security and accuracy within a defined parameter d, enabling secure two-party computation protocols.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fully homomorphic encryption schemes are used, then security is improved, but computational resources and complexity increase significantly
Solution Approach 1:
The patent segments the homomorphic encryption functionality into two distinct schemes: a first somewhat homomorphic encryption scheme that supports addition operations, and a second somewhat homomorphic encryption scheme that supports multiplication operations. This segmentation allows each scheme to be optimized for its specific operation type, reducing the overall computational complexity compared to a single fully homomorphic encryption scheme while maintaining security through the combination of both schemes.
2Device complexity
If somewhat homomorphic encryption schemes are used, then computational resources are reduced, but the number of homomorphic operations is limited due to noise accumulation
Solution Approach 1:
The patent introduces a conversion mechanism that acts as an intermediary between the first and second somewhat homomorphic encryption schemes. This conversion allows ciphertexts encrypted under the first scheme (supporting addition) to be transformed into ciphertexts encrypted under the second scheme (supporting multiplication), and vice versa. This intermediary conversion process enables the system to perform multiple alternating addition and multiplication operations while managing noise accumulation, thereby increasing the total number of homomorphic operations that can be performed.
3Measurement precision
If noise management is implemented to maintain security, then accuracy is preserved, but the number of operations is constrained by parameter d
Solution Approach 1:
The patent utilizes parameter changes by switching between two different encryption schemes with different operational characteristics. The first scheme is optimized for addition operations with specific noise properties, while the second scheme is optimized for multiplication operations with different noise properties. By changing the parameter (which encryption scheme is active) based on the operation type and noise level, the system can perform more operations while maintaining accuracy, as each scheme operates within its optimal noise tolerance range.
Data Source
AI summary
In one embodiment, data for use by a processor is stored in a memory. A network interface communicates over a network with a second device. At a processor, a Somewhat Homomorphic Encryption (SHE) of a plurality of secret shares is generated. The SHE of the plurality of secret shares is sent to the second device. The following is performed in a loop: a first result of a homomorphic exclusive-or operation performed by the second device on the SHE is received, a SHE of the first result is performed, yielding a second result, a SHE of the second result is performed yielding a third result, the third result is transmitted to the second device, and a final SHE result is received from the second device. The received final SHE result is decrypted in order to produce a final Somewhat Homomorphically Decrypted (SHD) output. The final SHD output is then output. Related methods, systems, and apparatus are also described.